How to loop in a loopless language (Y Combinator)

In lambda calculus, you need recursion to do looping, and this is done using the Y Combinator formula.
Lambda Calculus Video:    • Why functions are turing complete (Lambda ...  

For those unaware, lambda calculus is a turing complete programming language invented before computers ever existed. It is extremely simple and has an esoteric feel while having been invented as a serious mathematical model.